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In solving linear equations, one of the core concepts is to isolate the variable. This means getting the variable by itself on one side of the equation. Let's break down what this means.
To isolate the variable in the equation, we need to perform operations that allow us to remove any constants or coefficients attached to the variable.
For instance, in the equation \(n + 6 = 5\), we focus on the term with the variable 'n'. Here, 'n' is being added to 6.
To get 'n' by itself, we do the opposite of adding 6, which is subtracting 6. This keeps the balance of the equation, meaning what we do to one side, we must do to the other side too.
So if we subtract 6 from both sides, it looks like this :

• + 6 - 6 = 5 - 6

Now we have successfully isolated the variable 'n'.

Once the variable is isolated, the next step is to simplify both sides of the equation.
In the example \(n + 6 - 6 = 5 - 6\), we have:

• Subtraction of 6 from both sides of the equation.

On the left side of the equation, adding and then subtracting 6 cancels out to zero, leaving us with 'n'.
On the right side of the equation, we perform the subtraction:

• \(5 - 6 = -1\)

So after simplifying both sides, we are left with:

• \(n = -1\)

Simplifying both sides ensures that we have the simplest possible form of the equation where the solution is clear and easy to understand.

Understanding basic algebra is essential for solving equations like \(n + 6 = 5\). Algebra involves using variables (like 'n') to represent unknown values and performing operations (like addition, subtraction, multiplication, and division) to find the value of these variables.
The key principles of basic algebra include:

• Maintaining the balance of an equation: What you do to one side, you must also do to the other side.
• Using opposite operations to isolate the variable: For instance, if something is added to the variable, we subtract the same value to cancel it out.

In our example, we used subtraction to remove 6 from the left side, isolating 'n'. Understanding these basic algebraic operations helps in solving more complex equations in the future.
By mastering these foundational concepts like isolating the variable, simplifying both sides, and basic algebra, you will gain a strong understanding of how to solve linear equations confidently.